The Rangers began the reconstruction of their left side by signing Chris Simon yesterday – and the next step could be the reacquisition of Jan Hlavac, The Post has learned.

Addition of the 31-year-old Simon is a gamble, given the downward trajectory of his career; but bringing back Hlavac to play with Petr Nedved and right-winger Alex Kovalev should be a no-brainer.

While so many of the Rangers’ acquisitions have turned in their weakest performances on Broadway, Hlavac gave the Blueshirts his best – scoring 47 goals in two seasons, while producing only 26 in two seasons since.

The Rangers reportedly have been in close contact with Rich Winter, who represents Hlavac, and are negotiating a one-year deal in the neighborhood of $800,000. Hlavac is also considering an offer to remain in Europe, according to sources close to the situation.

Hlavac, who played with Nedved and Radek Dvorak on the productive “Czechmate” unit, scored 28 goals in 2000-01, but has bounced from Philadelphia to Vancouver to Carolina since leaving in the trade for Eric Lindros.

Hlavac, who turns 27 in September, became a free agent when the Hurricanes failed to make him a qualifying offer. He earned $1.65 million last season – just $150,000 more than the Rangers will pay Simon, who appears at first blush to be another gun hired well past his prime.

Once a feared physical force, the 6-foot-4, 235-pound Simon was a contributor to the 1996 Stanley Cup-champion Avalanche, but has done little of note since scoring 29 goals for the Caps in 1999-2000. Dealt early last year to Chicago, Simon collected 20 points (12-8) with 148 penalty minutes, while averaging 10:46 of ice in 71 games.

But Glen Sather has always liked Simon. Indeed, the Rangers nearly obtained the winger at the 2001 deadline in a deal that would have procured him from Washington, along with Andrei Nikolishin and Richard Zednik, in exchange for Adam Graves and Rich Pilon. Simon, who is training in L.A. for the summer, met with Sather last week.